Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Local relativistic invariant flows for quantum fields

For quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the Lorentz group by automorphisms on a Banach space generated by the Weyl algebra.     

Local and global Markoff fields

We discuss the relation between local and global Markoff property for processes and (generalized) random fields, both in the case of discrete and continuous ”time parameters“. In particular, we give a short account of our proof of the global Markoff property for the Euclidean Sine-Gordon fields in two dimensions. We also give an account of our proof of the uniqueness of the solutions of the DLR equations in this case (extremality of the Gibbs state, implying in particular uniqueness of the phase). We also discuss more generally the relation between the uniqueness and global Markoff properties, and discuss some consequences of the global Markoff property. Finally, we indicate shortly how the global Markoff property is proven (by ourselves together with G. Olsen) in the case of lattice systems.     

On rings generalizing commutativity

A class of rings is introduced and shown to be useful for obtaining deformation invariant equalities and commutativity results for some important algebras.     

Local models of spatio-temporally complex fields

We investigate the ability of local models of the one space dimensional Kuramoto-Sivashinsky partial differential equation with periodic boundary conditions, obtained by projection on a small set of Fourier modes on a short subinterval, to reproduce coherent events typical of solutions of the same equation on a much longer interval. We find that systems containing as few as two linearly unstable modes can produce realistic local events in the short term, but that for more reliable short time tracking and long term statistics, three or four interacting modes are required, and that the length of the short interval plays a subtle rôle, certain “resonant” lengths giving superior results.     

Local fields in single-mode helical fibres

The scalar local-field wave equations in helical fibres are derived and, with the aid of a special mathematical treatment, solved approximately in a local coordinate system—the Serret-Frenet frame from the Maxwell's equations. Two basic results are obtained: (1) The local modes in a single-mode helical fibre are circularly polarized. (2) The difference of the propagation constants between the two fundamental modes is 2, where is the torsion. They agree well with the known experimental measurements.     

Dispersion relations for the vertex function from local commutativity

Dispersion relations for the vertex function are derived which are valid when two of the scalar variables are arbitrary complex inside certain domains of the product of the complex planes and the third scalar variable is evaluated just below or just above the physical region-cut.The domains of validity of the dispersion relations for the complex variables are domains with three real dimensions and can be described as neighbourhoods of the boundaries of the axiomatic analyticity region of Källén and Wightman.The discontinuity of the vertex function across the cut-surface in the third variable for such values of the remaining variables is expressed only in terms of the dynamical on-mass-shell matrix elements of the locally commuting field operators.     

Local fields in a soft matter bubble

The electric field created by a point dipole located in a dielectric void (“bubble”) is calculated. We consider a continuous profile of the medium permittivity and find that, at large distances, the effective dipole field depends on the model chosen for the bubble walls, in particular their thickness. A boundary layer model is analyzed that gives good agreement with numerical calculations. Our results shed light on the local field correction that has attracted lot of interest lately.     

Local eddy current measurements in pulsed fields

This work presents new eddy current measurements in pulsed fields. A commercial point pick-up coil is used to detect the induction signal along the radius of Cu and Al samples with cylindrical shape and diameters between 5 and 35 mm. Local eddy current measurements were performed on the surface of conducting materials due to the small dimensions of the coil. A simple electrical circuit, used as a model, is proposed to describe the local eddy current effect in pulsed fields. The proposed model allows to calculate the phase shift angle between the signal proportional to eddy currents and the applied external field in a pulsed field magnetometer.     

Local fields on terbium nuclei in Tb-Y alloys

Data for terbium NMR (central transition) in Tb-Y alloys are presented. It was revealed that dilution of terbium by nonmagnetic yttrium slightly influences the local fields on terbium nuclci.     

A comment on Baxter condition for commutativity of transfer matrices

LetT _N andT _N be the transfer matrices of two vertex models corresponding to two sets of Boltzmann weights. The Baxter condition on Boltzmann weights was known to be sufficient for commutativity ofT _N andT _N for allN. We show that generically it is also necessary.Partially supported by NSF Grant DMS-8403238.     

Local fields in Co and Mn Co-doped ZnO

The magnetic properties of ZnO co-doped with 5 at. % Co and 5 at. % Mn(Zn_0.90Co_0.05Mn_0.05O) synthesized by a solid-state reaction were investigated by means of ⁵⁷Co emission Mössbauer spectroscopy. The majority of the probe ions (80 %) residing in defect-free substitutional Zn sites take the oxidation state of ⁵⁷Fe ²⁺, and the others presumably form local defects taking the state of ⁵⁷Fe ³⁺ at room temperature. Both components show doublets, and RT ferromagnetism was thus absent in the sample. For the measurement at 10 K, spectral broadening was observed, implying a possible presence of a weak magnetic component.     

Local fields at positive muons in magnetic substances

The various contributions to the local field at a positive mouon in ferro- and antiferromagnetic substances are discussed. Formulas for the calculation of the dipolar field tensors are derived. The influence of the oscillation of the muon around its equilibrium site is analyzed.Supported in part by the Swiss National Science Foundation.     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

Another comment on the Baxter condition for commutativity of transfer matrices

The Baxter condition has long been known to be sufficient for commutativity of transfer matrices. It was shown earlier that under an invariant subspace assumption the Baxter condition is also necessary. Although the invariant subspace condition holds genericly, it is very awkward to verify. Here we replace it by a symmetry condition. Namely we show that if the Boltzmann weights of two vertex models possess certain symmetry then the Baxter condition is necessary for commutativity of their transfer matrices.     

Local fields near the surface of a crystalline dielectric

We calculate the variation of the local electric field with depth near the surface of a crystalline dielectric, for the cases of induced atomic dipoles oriented perpendicular and parallel to the surface. The crystalline dielectric is modelled by a cubic lattice of polarizable atoms, with the surface in the (001) plane. Our calculations show that the departure of the local field from its bulk value is confined almost entirely to the outermost plane, and even there is small (at the most a few percent).